This question is not so much about Letterhead supporting emojis, but rather, email support of emojis, in general.
Although Letterhead supports any emojis, we have found that the emojis that work best across email clients are any from Emoji 1.0.
You can copy and paste from Emoji 1.0 directly into your newsletter.
Please note: There is no guarantee that emojis in this list will render across all email clients, but this is the safest list.